Computer Axial Tomography (CAT), sometimes known generally as Computerized Tomography (CT), is used in many applications, especially medical radiology, to obtain two or three dimensional views of the interior of three dimensional bodies (CT or CAT Scans). The technique involves subjecting a three dimensional body to radiation that enters the body from many different angles. The amount of radiation that is scattered or reflected by the body is then detected as a function of the angle of scattering. The scattered data is then analyzed to construct an image of the interior of the body. A two dimensional “slice” of the interior can be “reconstructed”, for example on a screen, and viewed. The slice can be reconstructed for any desired angle of intersection with the body.
While computerized tomography is well known, various specific mathematical reconstruction algorithms have been proposed to construct the image from the scattered radiation. However, it is becoming more challenging for known conventional reconstruction methods to meet the stringent constraints of current imaging applications. For example, the rates at which the impinging radiation beam scans the body has increased dramatically over the years, and the impinging radiation dosage has dropped significantly, especially in medical applications, because of patient safety concerns.
Two of the most common reconstruction algorithms that were developed to meet the stringent constraints of current imaging applications are the Filtered Back Projection method (FBP, sometimes written Filtered Backprojection method) and the Iterative Reconstruction Method (IR). In FBP, as a radiation detector rotates around the body being exposed to radiation, it detects and creates a series of planar images. Each of these images is a projection of the entire body mass for a particular angle, much as a common medical X-ray image. At each angle that the camera makes with the body, only radiation moving perpendicular to the camera is detected. As much of this radiation originates from various depths in the body, the result is an overlapping of the images of all elements of the body along the specific path, much in the same manner that a medical X-ray radiograph is a superposition of all anatomical structures from three dimensions into two dimensions.
An FBP study consists of many of such planar images acquired at various angles. After all the projections are acquired, they are subdivided by taking all the projections for a single, thin slice of the body at a time. All the projections for each slice are then ordered into an image called a sinogram. It represents the projection of the radiation distribution in the body for that single slice for every angle of the acquisition. The aim of the process is to retrieve the spatial distribution of the radiation from the projection data, thereby obtaining a clearer image of the body.
The quality of the image is further improved by filtering the data, which is most easily performed in the frequency domain rather than the spatial domain using well know Fast Fourier Transform techniques (FFT). The filtered data is than transformed back to the spatial domain.
The main reconstruction step involves a process known as back projection. As the original data was collected by only allowing radiation emitted perpendicular to the camera face to enter the camera, back projection smears the data from the filtered sinogram back along the same lines from where the radiation was emitted. Regions where back projection lines from different angles intersect represent areas which are of particular interest.
FBP and FFT-based reconstruction methods are popular in commercial CT scanners for their efficiency and accurate results when enough projection data is available. However, to lower the X-ray dosage (i.e., in low-dose CT imaging), the signal-to-noise ratio and the number of projections are reduced, which often results in undesirable “streaking artifacts”. There are typically two main sources of streaking artifacts First, the filter may amplify the imaging noise in the sinogram, which often produces streaking lines during back projection. Second, strong sharp edges, caused by, e.g., metal or bones, are back projected along the projection direction, causing streaking artifacts, especially when the number of projections is limited. Streaking noise is signal dependent and spatial variant, often making it extremely difficult to model this artifact accurately and distinguish the noise from true edges in the image. In the field of medical radiology, this typically results in difficult and/or inconsistent clinical interpretation(s).
The second reconstruction technique mentioned above, the Iterative Reconstruction (IR) method, can often produce a better reconstruction when FBP does not yield an acceptable solution. There are a large variety of IR algorithms, but each starts with an assumed image, computes projections from the image, compares the original projection data and updates the image based upon the difference between the calculated and the actual projections. Although conceptually this approach is typically simpler than FBP, for medical applications, it has traditionally lacked the speed of implementation and accuracy. This is due to the slow convergence of the algorithm and high computational demands. For these reasons, it was superseded by the FBP method in the early development of CT.
Therefore, there remains a need to more efficiently and accurately reconstruct an image using FBP, especially in low-dose CT.